A Bayesian approach to energy monitoring optimization

Abstract:

This thesis develops methods for reducing energy Measurement and Verification (M&V) costs through
the use of Bayesian statistics. M&V quantifies the savings of energy efficiency and demand side
projects by comparing the energy use in a given period to what that use would have been, had no
interventions taken place. The case of a large-scale lighting retrofit study, where incandescent lamps
are replaced by Compact Fluorescent Lamps (CFLs), is considered. These projects often need to be
monitored over a number of years with a predetermined level of statistical rigour, making M&V very
expensive.
M&V lighting retrofit projects have two interrelated uncertainty components that need to be addressed,
and which form the basis of this thesis. The first is the uncertainty in the annual energy use of the
average lamp, and the second the persistence of the savings over multiple years, determined by the
number of lamps that are still functioning in a given year. For longitudinal projects, the results from
these two aspects need to be obtained for multiple years.
This thesis addresses these problems by using the Bayesian statistical paradigm. Bayesian statistics is
still relatively unknown in M&V, and presents an opportunity for increasing the efficiency of statistical
analyses, especially for such projects.
After a thorough literature review, especially of measurement uncertainty in M&V, and an introduction
to Bayesian statistics for M&V, three methods are developed. These methods address the three types
of uncertainty in M&V: measurement, sampling, and modelling. The first method is a low-cost energy
meter calibration technique. The second method is a Dynamic Linear Model (DLM) with Bayesian
Forecasting for determining the size of the metering sample that needs to be taken in a given year.
The third method is a Dynamic Generalised Linear Model (DGLM) for determining the size of the
population survival survey sample.
It is often required by law that M&V energy meters be calibrated periodically by accredited laboratories.
This can be expensive and inconvenient, especially if the facility needs to be shut down for meter
installation or removal. Some jurisdictions also require meters to be calibrated in-situ; in their operating
environments. However, it is shown that metering uncertainty makes a relatively small impact to
overall M&V uncertainty in the presence of sampling, and therefore the costs of such laboratory
calibration may outweigh the benefits. The proposed technique uses another commercial-grade meter
(which also measures with error) to achieve this calibration in-situ. This is done by accounting for the
mismeasurement effect through a mathematical technique called Simulation Extrapolation (SIMEX).
The SIMEX result is refined using Bayesian statistics, and achieves acceptably low error rates and
accurate parameter estimates.
The second technique uses a DLM with Bayesian forecasting to quantify the uncertainty in metering
only a sample of the total population of lighting circuits. A Genetic Algorithm (GA) is then applied
to determine an efficient sampling plan. Bayesian statistics is especially useful in this case because
it allows the results from previous years to inform the planning of future samples. It also allows for
exact uncertainty quantification, where current confidence interval techniques do not always do so.
Results show a cost reduction of up to 66%, but this depends on the costing scheme used. The study
then explores the robustness of the efficient sampling plans to forecast error, and finds a 50% chance
of undersampling for such plans, due to the standard M&V sampling formula which lacks statistical
power.
The third technique uses a DGLM in the same way as the DLM, except for population survival
survey samples and persistence studies, not metering samples. Convolving the binomial survey result
distributions inside a GA is problematic, and instead of Monte Carlo simulation, a relatively new
technique called Mellin Transform Moment Calculation is applied to the problem. The technique is
then expanded to model stratified sampling designs for heterogeneous populations. Results show a
cost reduction of 17-40%, although this depends on the costing scheme used.
Finally the DLM and DGLM are combined into an efficient overall M&V plan where metering and
survey costs are traded off over multiple years, while still adhering to statistical precision constraints.
This is done for simple random sampling and stratified designs. Monitoring costs are reduced by
26-40% for the costing scheme assumed.
The results demonstrate the power and flexibility of Bayesian statistics for M&V applications, both in
terms of exact uncertainty quantification, and by increasing the efficiency of the study and reducing
monitoring costs.